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Filter Cascade

Combine filters in series - magnitudes multiply, phases add

Low-Pass

Butterworth

→

Notch

60 Hz reject

→

High-Pass

DC blocking

→ Output
Low-Pass
Notch
High-Pass
Combined (thick)
0.40π
0.15π
0.05π

Cascading Filters

Magnitude: |H_total(ω)| = |H₁(ω)| × |H₂(ω)| × |H₃(ω)| - Multiply in linear domain, add in dB

Phase: ∠H_total(ω) = ∠H₁(ω) + ∠H₂(ω) + ∠H₃(ω) - Phases always add

Common Use Cases:

• Band-pass = Low-pass + High-pass cascaded

• Anti-aliasing = Multiple stages for sharper rolloff

• Signal conditioning = DC blocking + notch + smoothing